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If x ≥ 0.9, which of the following could be the value of 1/(x^(1/2))

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Bunuel
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If x ≥ 0.9, which of the following could be the value of 1/(x^(1/2)) [#permalink] New post   20 Sep 2018, 00:57
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If x ≥ 0.9, which of the following could be the value of \(\frac{1}{\sqrt{x}}\)?

(A) 1.02
(B) 1.12
(C) 1.23
(D) 1.45
(E) 2.1
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A
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If x ≥ 0.9, which of the following could be the value of 1/(x^(1/2)) [#permalink] New post   20 Sep 2018, 03:05
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Bunuel wrote:
If x ≥ 0.9, which of the following could be the value of \(\frac{1}{\sqrt{x}}\)?

(A) 1.02
(B) 1.12
(C) 1.23
(D) 1.45
(E) 2.1


Do we require to solve it.....NO

The question can have only two extremes as the answer, so it will be A or E. If the question finally means MAX possible, it will be the lowest so A AND if it means minimum possible, ans is E
So what can be the best way without any calculations..
x is increasing, so √x will also increase as we are generally looking at the value of X above 1..
If √x is increasing, \(\frac{1}{√x}\) will decrease. So we are looking for the MAX possible
So if there is ONLY one choice that fits in, it will be the smallest, so A.
Say if B was possible, then A being smaller would surely be possible too.

A
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Re: If x ≥ 0.9, which of the following could be the value of 1/(x^(1/2)) [#permalink] New post   20 Sep 2018, 06:36
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Bunuel wrote:
If x ≥ 0.9, which of the following could be the value of \(\frac{1}{\sqrt{x}}\)?

(A) 1.02
(B) 1.12
(C) 1.23
(D) 1.45
(E) 2.1



In general, it is handy to know that

for \(0 < x < 1\), \(x < \sqrt{x} < 1\)

for \(x > 1\), \(1 < \sqrt{x} < x\)

Using these properties,

For \(x = 0.9\) , we know \(\sqrt{x} < 1\), hence \(\frac{1}{\sqrt{x}} > 1\)

\(\frac{1}{\sqrt{x}}\) = \(\sqrt{{\frac{10}{9}}}\) = \(\sqrt{1.11}\)

For \(x = 1\), we get, \(\frac{1}{\sqrt{x}} = 1\)

For any \(x > 1\), we get, \(\frac{1}{\sqrt{x}} < 1\)

Hence out of the answer choices, the only value less than 1.11 is 1.02

Answer A.


Thanks,
GyM
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If x ≥ 0.9, which of the following could be the value of 1/(x^(1/2)) [#permalink] New post   20 Sep 2018, 21:34
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Bunuel wrote:
If x ≥ 0.9, which of the following could be the value of \(\frac{1}{\sqrt{x}}\)?

(A) 1.02
(B) 1.12
(C) 1.23
(D) 1.45
(E) 2.1


\(x ≥ 0.9\)
i.e. \(1/x ≤ 1/0.9\)
i.e. \(1/x ≤ 1.11\)
taking square root both sides
i.e. \(√(1/x) ≤ √1.11\)
i.e. \(√(1/x) ≤ 1.11\)

Answer:Option A

CONCEPT: For any value of x such that 0 < x < 1, The square root of the value will be bigger than value i.e. \(√x > x\) and square will be smaller than value i.e. \(x^2 < x\)
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Re: If x ≥ 0.9, which of the following could be the value of 1/(x^(1/2)) [#permalink] New post   19 Aug 2019, 09:11
Bunuel wrote:
If x ≥ 0.9, which of the following could be the value of \(\frac{1}{\sqrt{x}}\)?

(A) 1.02
(B) 1.12
(C) 1.23
(D) 1.45
(E) 2.1


given: since x≥0.9 we can simplify the fraction by squaring
\(\frac{1}{\sqrt{x}}=\frac{1^2}{\sqrt{x^2}}=\frac{1}{x}\)
\(\frac{1}{x}=\frac{1}{9/10}=\frac{10}{9}≤1.12\)

Answer (A).
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If x ≥ 0.9, which of the following could be the value of 1/(x^(1/2)) [#permalink] New post   19 Aug 2019, 10:21
Bunuel wrote:
If x ≥ 0.9, which of the following could be the value of \(\frac{1}{\sqrt{x}}\)?

(A) 1.02
(B) 1.12
(C) 1.23
(D) 1.45
(E) 2.1


Given: x ≥ 0.9

Asked: Which of the following could be the value of \(\frac{1}{\sqrt{x}}\)?

x ≥ 0.9
\(\sqrt{x} ≥ \sqrt{0.9} = \sqrt{9/10} = 3/\sqrt{10}\)

\(\frac{1}{\sqrt{x}} \leq \sqrt{10}/3 = 3.16/3 = 1.05\)

IMO A
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Re: If x 0.9, which of the following could be the value of 1/(x^(1/2)) [#permalink] New post   02 Apr 2024, 03:54
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Re: If x 0.9, which of the following could be the value of 1/(x^(1/2)) [#permalink]
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